President Donald Trump dispatched the director of the CIA to Turkey in a quest to get more information about the death of Saudi writer Jamal Khashoggi and weigh a possible US response.

Trump said Monday he was not satisfied with the explanations he's heard about the Washington Post columnist and critic of the kingdom who died on October 2 at the Saudi Consulate in Istanbul.

Saudi Arabia has said he was killed in a fistfight, but Turkish President Recep Tayyip Erdogan said Tuesday that Khashoggi's death was part of a planned operation.

"It appears, on the eve of the murder, 15 Saudi security personnel, intelligence officials and a forensics expert arrived in our country," Erdogan said. "It has been ascertained that six of them left on Oct. 2" later that evening on two planes.

"The Saudi Arabian administration has taken an important step by admitting the murder," Erdogan said. "As of now we expect of them to openly bring to light those responsible from the highest ranked to the lowest and to bring them to justice."

On Monday, Trump told reporters at the White House: "We're going to get to the bottom of it. We have people over in Saudi Arabia now. We have top intelligence people in Turkey."

"We're going to know a lot over the next two days about the Saudi situation," said Trump. "It's a very sad thing."

The CIA declined to confirm that Gina Haspel, who directs the agency, is in Turkey. But a US official said she is in the country to review the case.

The official, who declined to disclose details about what Haspel is doing in Turkey, was not authorized to discuss the trip publicly and spoke only on condition of anonymity.

Trump spoke Sunday with Saudi Crown Prince Mohammed bin Salman, who is the son of Saudi King Salman.

"He says he is not involved nor is the king," Trump told USA Today in an interview aboard Air Force One Monday en route to a political rally in Texas.

The newspaper said Trump declined to say whether he believed the crown prince's denials. If their involvement was proven, Trump said: "I would be very upset about it. We'll have to see."

Trump characterised Khashoggi's incident as a "plot gone awry" and told the newspaper he didn't think the writer was deliberately lured into the consulate to be killed.

When he was asked late last week whether he thought Saudi Arabia's claim that Khashoggi died in a fistfight was credible, the president answered: "I do. I do."

That statement rankled members of Congress and former government officials who have accused Riyadh of trying to cover up the truth behind Khashoggi's death or hide any evidence that the kingdom, particularly the crown prince, authorized it.

Senator Rand Paul, R-Ky, who has been trying to coax Trump into ending arms sales to Saudi Arabia, said Monday that it's "laughable" to believe the crown prince was not involved in Khashoggi's death.

Trump said any US response should not involve scrapping billions of dollars in arms sales, which would hurt US defence industries and eliminate US jobs.

"I don't want to lose all of that investment that's being made in our country," he said.

White House press secretary Sarah Huckabee Sanders said Trump will continue to demand answers. "He'll make a determination on what he wants to do once he feels like he has all of the information that he needs," she said.

Whatever the US response, US ties with its Gulf ally have hit rough waters. The Khashoggi affair also has threatened to upend the relationship of Trump's son-in-law Jared Kushner with the crown prince.

The two men both in their 30s, both trusted aides of older, familial leaders struck a bond last spring and consulted with one another frequently in private calls in the months that followed.

The crown prince, who is known in diplomatic circles as "MBS," has drawn some praise in the West for his moves to modernize the kingdom and criticism for his government's arrests of rivals and critics.

Trump now plays down the relationship, saying the crown prince and Kushner are "just two young guys." But their back-channel relationship unnerved many in the Trump administration and Washington foreign policy establishment who feared that the White House was betting too big on the crown prince.

Kushner on Monday fended off criticism that the Trump administration was giving Saudi Arabia cover. He said administration officials have their "eyes wide open".

"We're getting facts in from multiple places and once those facts come in, the secretary of state will work with our national security team to help us determine what we want to believe, what we think is credible and what we think is not credible," Kushner told CNN.

Even Trump, however, acknowledges that Kushner's work on trying to craft peace between Israel and the Palestinians has been set back by Khashoggi's death. "There are a lot of setbacks. This is a setback for that," Trump told The Washington Post in a weekend phone interview.

Bruce Riedel, a former Middle East specialist for the CIA and National Security Council, said the Trump administration "desperately wants the Istanbul affair to go away and the MBS-Jared bromance obscured.